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Abstract

Quadratically nonlinear systems may be analyzed and synthesized by linear methods by exchanging an N-dimensional nonlinear problem for a 2N-dimensional linear formulation. This paper describes the basis for such linearization of a quadratic functional, and applies the method to partially coherent transilluminated optical systems.

References

Quadratic-filter theory is appropriate whenever a system to be studied includes an energy-flux measurement, or has available as the input signal only a second moment of the observed process, a class of problems in which optical systems include perhaps the most important examples.

G is not bilinear in (u,v). The terminology "dilinear" is introduced to represent the specific two-variable extension of a single variable function that allows the quadratically nonlinear filter of this discussion to be analyzed and synthesized by linear-transfer-function techniques.

The linearity of Eq. (20) is not dependent on the infinite-limit assumption.

Other

Quadratic-filter theory is appropriate whenever a system to be studied includes an energy-flux measurement, or has available as the input signal only a second moment of the observed process, a class of problems in which optical systems include perhaps the most important examples.

G is not bilinear in (u,v). The terminology "dilinear" is introduced to represent the specific two-variable extension of a single variable function that allows the quadratically nonlinear filter of this discussion to be analyzed and synthesized by linear-transfer-function techniques.

The linearity of Eq. (20) is not dependent on the infinite-limit assumption.

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